Then again, Batman has shown time and again that he goes out of the way to preserve the Joker's life, so who knows? I've always thought that Bruce is obsessed with preserving the Joker's life more than any other villain because the Joker is the most deplorable... thus Bruce feels so much more the opposite... honorable if you will... by refusing to take his life or contribute to his demise.

It's highly likely that he would have saved him. After all, Batman is a psychopath himself. His obsession with saving everyone is a form of insanity. No normal human being would let the Joker live if they were in Batman's position. Another proof for this is the second fight with Bane in Arkham Origins. Only someone with mental issues would've reanimated Bane after stopping his heart with the shockgloves.